Today I had the final exam of the lesson Mathematics I. There was a question that I want to know if I solved correctly the following limit.
$$\lim\limits_{n\to\infty}\left(\frac{n}{0^2+n^2} + \frac{n}{1^2+n^2} + \frac{n}{2^2+n^2} + \dots + \frac{n}{(n-1)^2+n^2}\right)$$
By using the summation symbol and integral method, I found the answer $\pi/4$ . Is my answer correct?
Answer
Your answer is correct; however, because you have only described your method of solution rather than shown it, it is not possible at this time to confirm whether or not your actual computation was without methodological or conceptual flaws. We can only say that the value of the quantity you wrote is in fact $\pi/4$ as claimed.
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